How to evaluate logarithmic functions?

This problem is the same base as the exponential and logarithmic mixed evaluation. This kind of question generally tests your familiarity with the operation of exponents and logarithms, and is generally not very difficult, but you need to grasp the main points. The calculation for this problem is as follows:

10^(lg20).(1 10) (What needs to be known here is that 1 10 can be seen as the minus 1 power of 10, i.e., 10 (-1).)

10^(lg20).10 (multiply exponents by bases, add exponents) 10 (lg20+ (logarithms multiply with bases), 10 (lg14) (logarithms have a logan=n (a>0 ,a≠1). ）

If you're not familiar with that formula, you can do it like this:

Req: 10 (lg14)=x

The logarithm of 10 on both sides is: LG10 (LG14)=LGX, which is obtained by the logarithmic algorithm: left=LG14=LGX=right.

Obviously, we can conclude that x=14.

If you are satisfied, you will be satisfied.

There is a formula for logarithm that is a logan=n (a>0 ,a≠1), and this problem is calculated using this formula.

10lg20×(1/10)

1. The operation formula of the logarithmic function is shown in the following figure:

2. According to the logarithmic formula, the example calculation is as follows:

A logarithm with a base of 10.

In mainland textbooks, it is called the commonly used logarithmic cherry blossom difference.

Such as: LG2

Calculated: For reference, please accept it with a smile.

Please see the face of the loss and click to enlarge: Bi Raid.

The logarithm with 10 as the base is called the common logarithm of the socks, or simply the logarithm, for the logarithm with other Ming numbers as the base, the Wang Zhao can use the formula of changing the bottom and using the common logarithm to solve. The logarithm of 1 is zero, and the logarithm of 10 is 1.

If the power of a to the n power is equal to n, and n is greater than zero, then n is called a base, the logarithm of n, a is the base, and n is the true number.

The calculation process is as follows:

log₂3lg3÷lg2

Logarithmic function properties:In general, if a(a>0, and a≠1) to the power of b is equal to n, then the number b is called the logarithm of the orange with a as the base n, denoted as logan=b, where a is called the base of the logarithm and n is called the true number.

The base number of the bottom hall should be "0" and ≠1 true number" 0, and when comparing the values of two functions: if the bases are the same, the larger the true number, the larger the function value. Liquid (a>1); If the bases are the same, the smaller the true number, the larger the function value. （0

Every student who is new to logarithmic knowledge has most doubts. Very good. This is the embodiment of the spirit of willing to delve into the best.

We know that 2 to the 3rd power = 4 to the 4th power = 16. In fact, this "power" is the name of our country in ancient times, and it is the title of concepts such as "area and volume". What is the practical significance of the power of 2?

No. Therefore, it should be called [power of 2]. The word "power" is now a simplified word, and the traditional Chinese character is a bald treasure cover at the top and a "curtain" character at the bottom.

It is a big cloth wrapped around the head, just like the big cloth wrapped around the heads of men in India and my Yunnan area. Use this word to portray the person who "covers" and "occludes, controls". 2 Like a man's head, like a great cloth.

That's what power means. It is a very important and crucial number, which controls the size of the whole value. The difference in it changes the value of the entire "square power".

After talking for a long time, what is this going to say? That is to say, the power of 2 is a "transcendent number", which cannot be calculated by "elementary mathematical methods", and cannot be obtained by addition, subtraction, multiplication, and division.

Anyway, this number should have! And it's between 8 and 16! Right.

That's it. Let's let the power of 2 = a. So, what is the logarithm of a base 2?

Actually, it is". Thus, in a sense, "logarithm is exponential".

In general, the value of a logarithmic function "cannot be found with elementary operations"! Therefore, in engineering calculations, it is generally "looking up common logarithmic tables", or using a computer, or using an advanced calculator to find the approximate value needed.

Further study of advanced mathematics, which has the knowledge of "progression". can solve your problem.

I'll send you a picture by the way. Maybe you get the idea. There is no end to science.

If it is an integer, it can be obtained directly.

For example, ln(e 2)=2 log2(16)=4 is not an integer, and you can only press the calculator or check the logarithmic table.

Is there anything else you don't understand?

Hello bold table superscript.

First of all, I will give you a formula: a (loga∧n)=n

Therefore 2a = log e in this questionto meet the topic

So a =1 2 (ln e.)

Take the logarithm of both sides at the same time.

2a = ln 1/2 = - ln 2

Yields a = - 1 2 ln 2

The logarithmic symbol below omits the bottom:

It is organized as follows:

log(3^(x+2))+log(x)=log(3+5x)log[x(3^(x+2))]=log(3+5x)x×(3^(x+2))=3+5x

3 x = 1 (3x) + (5 9), where x -3 5

In this case, in the same Cartesian coordinate system, as an image of y=3 x, y=1 (3x)+(5 9), the intersection point is the solution of the function.

Logarithmic properties:

logax=loga²x²

From this property it can be obtained:

log2(5)=log4(25)

From the "logarithmic identity", we get:

4^[log4(25)]=25.

4^[log2(5)]=4^[log4(25)]=25.

The specific process of answering Xiangfeng is as follows: trace nucleus.

Calculation results:

Hehe, can you add some points?